黑料社

Title:Proper Correlation Coefficients for Nominal Random Variables.

础产蝉迟谤补肠迟:听

This work develops an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale that is attainable for all marginal distributions and proposes a set of dependence measures that are 1 if and only if this perfect dependence is satisfied. The advantages of these dependence measures relative to classical dependence measures like contingency coefficients, Goodman-Kruskal鈥檚 lambda and tau and the so-called uncertainty coefficient are twofold. Firstly, they are defined if one of the variables is real-valued and exhibits continuities. Secondly, they satisfy the property of attainability. That is, they can take all values in the interval [0,1] irrespective of the marginals involved. Both properties are not shared by the classical dependence measures which need two discrete marginal distributions and can in some situations yield values close to 0 even though the dependence is strong or even perfect. Additionally, this work provide a consistent estimator for one of the new dependence measures together with its asymptotic distribution under independence as well as in the general case. This allows to construct confidence intervals and an independence test, whose finite sample performance is subsequently examine in a simulation study. Finally, we illustrate the use of the new dependence measure in two applications on the dependence between the variables country and income or country and religion, respectively.

Speaker

Lukas Wermuth studied Economics and Mathematics at Goethe University Frankfurt, where he is currently pursuing a PhD in Statistics and Econometrics.